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# Meusnier's theorem

In differential geometry, Meusnier's theorem states that all curves on a surface passing through a given point p and having the same tangent line at p also have the same normal curvature at p and their osculating circles form a sphere. The theorem was first announced by Jean Baptiste Meusnier in 1776.

References

Meusnier's theorem Johannes Kepler University Linz, Institute for Applied Geometry

Meusnier's theorem in Springer Online

Ian R. Porteous (2001) Geometric Differentiation, § 15.1 Theorems of Euler and Meusnier, pp 253–5, Cambridge University Press ISBN 0-521-00264-8 .

Undergraduate Texts in Mathematics

Graduate Studies in Mathematics

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